Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in CPP):

Solution:
#include "bits/stdc++.h"
#define rep(i,a,n) for(int i = a;i < n;i++)
typedef unsigned long long ull;
typedef long long ll;
using namespace std;

int main(){
    ll n,deff = 0,memo1,memo2,sum = 0,cnt = 0;
    cin >> n;
    ll a[n];
    double maxi = 0;
    
    rep(i,0,n){
        cin >> a[i];
    }
    
    sort(a,a+n);
    
    rep(i,1,n){
        deff = a[i] - a[i-1];
        memo1 = i;
        memo2 = i-1;
        sum = 0; cnt = 0;
        rep(j,0,n){
            if(!(memo1 == n-j-1 || memo2 == n-j-1) && cnt < 2){
                sum += a[n-j-1];
                cnt++;
            }
            else if(cnt >= 2){
                break;
            }
        }
        
        maxi = max(maxi,(double)sum/(double)deff);
    }
    
    
    cout << setprecision(20) << maxi << endl;
    return 0;
}